I'm not the original poster, but I'd guess they might have had the same thought I did, of the Count on Sesame Street saying "will you count with me." I was going to ask if this can mean that, too, but now that I think about it, isn't there another verb for actual number counting?
If I understand your question correctly: "Å regne med" is an idiom in Norwegian just like "to count on" is an idiom in English. And they are used in the exact same way, meaning either "to rely on" or "to expect/predict".
The verb "Å regne" by itself has a quite different meaning from the English verb "to count" though.
Me too. I was like "rain with me? No, that doesn't make sense". Luckily I tapped on the word and saw the translation "count".
Only then it dawned on me that we have a similar expression in german: "mit jemanden rechnen", which literally translates as "to calculate with someone".
The first one would be technically correct, and I quite enjoyed the picture you painted, but it's still too unlikely a scenario for us to accept here.
We always have to weigh the pros and cons of adding an acceptable translation, as they can show up as suggested translations for those who get their answer wrong. Sometimes it's better to disappoint one person than to confuse a thousand - even if we wish we could avoid both. :)
You can something like "Kan jeg regne med deg?" to mean "Can I count you in?" for participation in an activity. This works with "Skal jeg..." as well. However, it sounds quite stilted when adding "Vil du.." in front, so that's not something I'd recommend.
Norwegian has a lot of those, here's some of them: https://blogs.transparent.com/norwegian/norwegian-homonyms/